An excited hydrogen atom emits light with a wavelength of 486.4 nm to reach the energy level for which n = 2. In which principal quantum level did the electron begin?

The electron began in the quantum level of 4

Explanation:

Using the formula of wave number:

Wave Number = 1/λ = Rh (1/n1² - 1/n2²)

where,

Rh = Rhydberg's Constant = 1.09677 x 10^7 / m

λ = wavelength of light emitted = 486.4 nm = 486.4 x 10^-9 m

n1 = final shell = 2

n2 = initial shell = ?

Therefore,

1/486.4 x 10^-9 m = (1.09677 x 10^7 / m) (1/2² - 1/n2²)

1/4 - 1 / (486.4 x 10^-9 m) (1.09677 x 10^7 / m) = 1/n2²

1/n2² = 0.06082

n2² = 16.44

n2 = 4